Robust and accurate proprioceptive state estimation of the main body is crucial for legged robots to execute tasks in extreme environments where exteroceptive sensors, such as LiDARs and cameras, may become unreliable. In this paper, we propose DogLegs, a state estimation system for legged robots that fuses the measurements from a body-mounted inertial measurement unit (Body-IMU), joint encoders, and multiple leg-mounted IMUs (Leg-IMU) using an extended Kalman filter (EKF). The filter system contains the error states of all IMU frames. The Leg-IMUs are used to detect foot contact, thereby providing zero-velocity measurements to update the state of the Leg-IMU frames. Additionally, we compute the relative position constraints between the Body-IMU and Leg-IMUs by the leg kinematics and use them to update the main body state and reduce the error drift of the individual IMU frames. Field experimental results have shown that our proposed DogLegs system achieves better state estimation accuracy compared to the traditional leg odometry method (using only Body-IMU and joint encoders) across various terrains. We make our datasets publicly available to benefit the research community (https://github.com/YibinWu/leg-odometry).

The foot-mounted inertial navigation system (Foot-INS) is a crucial technology for professional pedestrian positioning, unaffected by environmental conditions. However, due to the unobservable nature of the absolute heading, single or dual Foot-INS configurations suffer from significant position drift errors. This paper introduces an innovative pedestrian dead reckoning (PDR) method that combines foot-mounted and waist-mounted IMU with magnetic field vector constraints. Leveraging the fact that the displacements of the foot and waist are consistent when the foot makes ground contact, the proposed method uses the relative displacement estimated by Foot-INS to correct the waist-mounted INS. Building on this, a relative magnetic field vector constraint method is developed using error state clonal Kalman filtering, capitalizing on the similarity of magnetic interference within a local area. The results from 12 tests conducted in typical indoor environments, such as offices and underground parking lots, demonstrate that the proposed method significantly enhances positioning performance in areas with frequent magnetic interference. The positioning error is reduced by more than 49% compared to single or dual Foot-INSs.

Pedestrian navigation using smart devices has become increasingly prevalent in daily life. Typically, the user’s location in outdoor environments can be obtained via the embedded global navigation satellite system (GNSS) chip. However, in urban environments, the performance of conventional GNSS positioning is significantly degraded due to multipath effects and non-line-of-sight (NLOS) receptions that ruin the GNSS observations. To address this challenge, this paper proposes a robust GNSS/inertial navigation system (INS) integrated system for pedestrian navigation in urban environments. Based on robust optimization algorithm, the proposed method utilizes the spatial consistency between multiepoch GNSS pseudorange observations and pedestrian dead reckoning (PDR) trajectory to detect GNSS outliers. Then, the fault-free GNSS observations are integrated with INS-based PDR via the conventional robust Kalman filter (RKF) in tightlycoupled mode. To validate the performance of the proposed method, nine sets of test data were collected covering three typical urban scenarios. Experimental results show that the proposed method achieves an average horizontal positioning accuracy of 10.21 m (95%), compared to 17.27 m for the conventional RKF, representing an improvement of approximately 41

Accurate and rapid INS state initialization is crucial to ensure the performance of vehicular GNSS/INS integrated navigation. However, in typical urban environments (such as under viaducts and urban canyons), existing GNSS-assisted INS state initialization methods are sensitive to observation outliers. This paper proposes a robust INS state initialization method for vehicle-mounted GNSS/INS integrated navigation. The proposed method first derives the error propagation between the short-term relative navigation (i.e., position, velocity, attitude) and the INS initial state and the GNSS observation error model; then, the high-precision relative pose generated by INS is used to construct constraints between GNSS observation sequences, and the INS state initialization problem is converted into an optimization problem; finally, a two-step optimization strategy is designed to improve the problem of high computational complexity in solving the full-state optimization problem. We use six datasets collected in a typical urban environment to verify the feasibility of the proposed method. The proposed method uses observation sequences within a 10-second to initialize the heading, velocity, and horizontal position with errors of 2.50∘, 0.30 m/s, and 11.1 m, respectively, which are reduced by 73%, 41%, and 14% compared with existing methods.

Location-based services (LBS) have become an integral part of daily life and work for the general public. However, achieving widespread and accurate positioning in typical indoor environments remains a significant challenge, particularly in multi-floor indoor parking lots where radio frequency signals like WiFi are often unavailable. Indoor magnetic matching presents a viable solution, but it requires reducing mapping costs through the use of crowdsourced data. To tackle this issue, we propose an innovative method for constructing magnetic maps using crowdsourced vehicle data. Our approach introduces a multi-user joint vehicle dead reckoning technique based on graph optimization, which provides consistent directional estimates of crowdsourced vehicle trajectories. Subsequently, we establish associations between different vehicle trajectories using multi-attribute features of the magnetic field. Building on this foundation, we propose a global trajectory optimization with inequality and equality constraints to achieve precise estimation of crowdsourced vehicle trajectories. Testing with simulated data from two three-floor underground parking lots demonstrates that the proposed method, utilizing only on-board smartphone sensor data, achieves plane and elevation errors of less than 2.75 meters (95%) and 0.59 meters (95%), respectively. Additionally, the magnetic matching positioning error based on crowdsourced magnetic sequence maps is less than 2.29 meters (95%).

A long-term accurate and robust localization system is essential for mobile robots to operate efficiently outdoors. Recent studies have shown the significant advantages of the wheel-mounted inertial measurement unit (Wheel-IMU)-based dead reckoning system. However, it still drifts over extended periods because of the absence of external correction signals. To achieve the goal of long-term accurate localization, we propose Wheel-GINS, a Global Navigation Satellite System (GNSS)/inertial navigation system (INS) integrated navigation system using a Wheel-IMU. Wheel-GINS fuses the GNSS position measurement with the Wheel-IMU via an extended Kalman filter to limit the long-term error drift and provide continuous state estimation when the GNSS signal is blocked. Considering the specificities of the GNSS/Wheel-IMU integration, we conduct detailed modeling and online estimation of the Wheel-IMU installation parameters, including the Wheel-IMU leverarm and mounting angle and the wheel radius error. Experimental results have shown that Wheel-GINS outperforms the traditional GNSS/Odometer/INS integrated navigation system during GNSS outages. At the same time, Wheel-GINS can effectively estimate the Wheel-IMU installation parameters online and, consequently, improve the localization accuracy and practicality of the system. The source code of our implementation is publicly available (https://github.com/i2Nav-WHU/Wheel-GINS).

Indoor positioning is an important part of supporting the Internet of Things and location-based services. Crowdsourcing-based magnetic map construction is a key technology to realize wide-area consumer indoor positioning. However, current crowdsourcing-based magnetic map schemes are not suitable for typical indoor scenarios (e.g., shopping malls). The reason is that they ignore the characteristics of crowdsourced data, including short-term trajectory, various pedestrian motion patterns, large-scale data set, and so on. In this article, we propose a novel crowdsourcing-based magnetic map construction method. First, learning-based inertial odometry is used to recover precise user motion trajectories regardless of changes in motion patterns. Then, a keyframe-efficient association method of magnetic time–frequency features is proposed, which is suitable for short-term trajectories of various shapes. Finally, a two-step global estimation optimization is proposed to further eliminate false associations of keyframes and improve the robustness of the method. The feasibility of the proposed method is verified by using a multiuser data set in a typical shopping mall scenario. The proposed method takes a total of 60.8 s to process a 12-h data set (subtrajectories with a duration of 90 s), and the average position error is 1.48 m (with scale correction) and 2.53 m (without scale correction). Compared with the existing crowdsourcing-based magnetic map scheme, the proposed method has been significantly improved in terms of feasibility, accuracy, and efficiency.

Lane-level positioning is a critical technology for supporting assisted driving and autonomous driving applica-tions. However, the Global Navigation Satellite System often falls short in providing reliable positioning (GNSS) due to signal attenuation, obstructions, and multipath in urban areas. Fortunately, typical challenging urban environments, such as tunnels and viaducts, create rich magnetic field features due to abundant ferromagnetic structures, offering an opportunity for magnetic field matching methods to achieve high-precision positioning. This paper presents a novel magnetic field matching/GNSS/Inertial Navigation System (INS) fusion algorithm designed for continuous lane-level positioning in complex environments using cost-effective sensors and computation-saving algorithm. Based on the traditional GNSS/INS tight integration algorithm, this research ensures the performance of the positioning system by enhancing the magnetic field matching and fusion positioning algorithms. First, a coarse-fine magnetic profile matching method is proposed to address the accuracy degradation resulting from the travel distance error of INS-derived trajectory. Second, the magnetic field matching position updates are performed in the vehicle frame, which enables more precise position error modeling. The proposed solution is evaluated through five field tests, covering over 200 kilometers of challenging urban roads. The results demonstrate mean CDF95 position errors of 2.09 m, 1.09 m, and 0.87 m in the forward, lateral, and vertical directions, respectively, and 94.67% accuracy on lane-determination.

Foot-mounted inertial navigation system (Foot-INS) with the zero velocity update (ZUPT) has become one of the indispensable technical means in professional pedestrian positioning fields due to the advantages of self-constraint and immune to environmental factors. The dual-Foot-INS can provide more excellent autonomous positioning performance than a single-Foot-INS because it utilizes more opportunities for zero velocity correction and additional distance constraint information. However, the classical dual-Foot-INS does not fully exploit the distance constraint potential for positioning improvement. In this article, we proposed a novel minimum distance constraint (MDC) method that achieves higher positioning accuracy than the traditional dual-Foot-INS methods. To obtain an accurate and consistent state estimation under the nonlinear distance constraint problem, we propose an iterative distance constraint (IDC) algorithm. The IDC is transformed into an approximate linear constraint model, and an alternative estimate is obtained by the estimation projection method. To solve the problem that the distance constraint moment in the traditional method is affected by the recursive foot positions, we propose a more reasonable and reliable minimum distance moment detection (MDMD) method. The proposed MDMD method maximizes the positioning performance improvement of the dual-foot pedestrian system. Two rigorous experimental tests with a long walking trajectory without turn around and closed loop were conducted to verify the effectiveness of the proposed method, the positioning error of the proposed method is reduced by 83.5% and 62.9% compared to the classical ZUPT and MDC methods, respectively.

The 3-D position estimation of pedestrians is a vital module to build the connections between persons and things. The traditional gait model-based methods cannot fulfill the various motion patterns. And the various data-driven-based inertial odometry solutions focus on the 2-D trajectory estimation on the ground plane, which is not suitable for augmented reality (AR) applications. Tight learned inertial odometry (TLIO) proposed an inertial-based 3-D motion estimator that achieves very low position drift by using the raw inertial measurement unit (IMU) measurements and the displacement prediction coming from a neural network to provide low drift pedestrian dead reckoning. However, TLIO is unsuitable for mobile devices because it is computationally expensive. In this article, a lightweight learned inertial odometry network (LLIO-Net) is designed for mobile devices. By replacing the network in TLIO with the LLIO-Net, the proposed system shows a similar level of accuracy but remarkable efficiency improvement. Specifically, the proposed LLIO algorithm was implemented on mobile devices and compared the computational efficiency with TLIO. The inference efficiency of the proposed system is up to 12 times improved than that of TLIO. Source code can be found onhttps://github.com/i2Nav-WHU/LightweightLearnedInertialOdometergithub.

A reliable self-contained navigation system is essential for autonomous vehicles. Based on our previous study on Wheel-INS[1], a wheel-mounted inertial measurement unit (Wheel-IMU)-based dead reckoning (DR) system, in this paper, we propose a multiple IMUs-based DR solution for the wheeled robots. The IMUs are mounted at different places on the wheeled vehicles to acquire various dynamic information. In particular, at least one IMU has to be mounted at the wheel to measure the wheel velocity and take advantage of the rotation modulation. The system is implemented through a distributed extended Kalman filter structure where each subsystem (corresponding to each IMU) retains and updates its own states separately. The relative position constraints between the multiple IMUs are exploited to further limit the error drift and improve the system’s robustness. Particularly, we present the DR systems using dual Wheel-IMUs, one Wheel-IMU plus one vehicle body-mounted IMU (Body-IMU), and dual Wheel-IMUs plus one Body-IMU as examples for analysis and comparison. Field tests illustrate that the proposed multi-IMU DR system outperforms the single Wheel-INS in terms of both positioning and heading accuracy. By comparing with the centralized filter, the proposed distributed filter shows unimportant accuracy degradation while holding significant computation efficiency. Moreover, among the three multi-IMU configurations, the one Body-IMU plus one Wheel-IMU design obtains the minimum drift rate. The position drift rates of the three configurations are 0.82% (dual Wheel-IMUs), 0.69% (one Body-IMU plus one Wheel-IMU), and 0.73% (dual Wheel-IMUs plus one Body-IMU), respectively.

Acquiring accurate and reliable pedestrian trajectories is essential for providing indoor location-based services. Although a foot-mounted inertial navigation system (Foot-INS) can acquire pedestrian trajectories in multistory buildings, it will inevitably encounter heading divergence because the constraint information is not always valid. Therefore, we proposed an accurate and convenient postprocessing indoor pedestrian positioning system (IPPS) to acquire pedestrian trajectories in multistory buildings such as shopping malls. Based on the hypotheses that the start and end points of the pedestrian trajectories on a single floor were closed, and the horizontal position of the closing point on each floor was identical. Therefore, in the single floor of multistory buildings, we use the closing point to control the trajectory drift error caused by the Foot-INS, and use a smoothing algorithm to reasonably distribute the drift error to the entire trajectory. Heading divergence is unavoidable with the Foot-INS, result in the pedestrian trajectories acquired on different floors were rotationally offset. Because pedestrian trajectories can epitomize the building orientation and provide an opportunity to align those trajectories on multistory buildings, an algorithm was proposed to match the trajectories acquired on different floors. A hybrid simulation experiment was conducted using an accurate reference object to evaluate the positioning performance of the proposed IPPS. The effectiveness of acquiring pedestrian trajectories was also confirmed by various experimental tests in a large shopping mall. The study findings suggest that the proposed IPPS is self-contained, low cost, and has the potential for large-scale applications.

The wireless capsule endoscope (robot) has become more extensively used due to its comprehensive detection and patient-friendly experience. However, to provide better diagnostic information to medical staff, there is an urgent need for high-accuracy position information of capsule endoscopes during their working inside the human body. In this article, a capsule endoscopy positioning system using a magnetic sensor array is designed. It has two advantages. 1) Most of the existing magnetic positioning method needs to initialize the magnetic moment accurately, which is difficult to meet in practical applications. To solve this issue, this article proposes a method to determine the magnetic moment direction based on an inertial measurement unit. The proposed method can accurately estimate the direction of the magnetic moment even when the roll angle is singular. 2) This article proposes a nonlinear least-squares algorithm for capsule magnetic positioning based on the three-axis magnetometer observation. The algorithm is more robust than the Levenberg–Marquardt (LM) method that is widely used in capsule endoscopy positioning. Furthermore, its computation speed is over 100 times faster than the LM method, which successfully meets the real-time requirements. In this research, a three-axis mechanical platform and a six-axis robot arm are used to build a capsule magnetic positioning evaluation system. Preliminary results show the accuracy (RMS) of the proposed capsule endoscope positioning algorithm was better than 6 mm.